Thanks for some very useful advice which I'll keep on file for future reference - very new to these Mac thingy's but very please with them.
The upshot of the whole affair was that the dealership and I took a collective decision to send the machine back to Apple on Dec. 17th as it was within the 2-week "dead on arrival" period. They looked it over, decided that it was the battery at fault and not the machine, replaced the battery and shipped it back. I got it on Dec. 29th.
Now to me, bearing in mind the time of year, that's f____ing impressive service by anyone's standards.
Thanks again for the advice.